Keele Research Repository

For asymptotic observers, geodesic paths of radially inbound photons in a Schwarzschild space-time approach the critical radius of a collapsed star asymptotically. When considering processes of accretion or quantum evaporation however, inbound null geodesics, in a corresponding Vaidya space-time, pass through a momentary inflection point where time dilation diverges and subsequently reach the critical radius within a finite coordinate time. By considering a diagonal form of the Vaidya metric that reduces to the Schwarzschild metric in the zero accretion/evaporation limit, photons approaching on radial paths pass through the inflection point and undergo infrared divergence at the critical radius. Particles on radial timelike geodesics are shown to meet a potential barrier beyond the inflection point, which diverges at the critical radius.